(a+2b)(5a-4b)=0

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Solution for (a+2b)(5a-4b)=0 equation: 


Simplifying
(a + 2b)(5a + -4b) = 0

Multiply (a + 2b) * (5a + -4b)
(a(5a + -4b) + 2b * (5a + -4b)) = 0
((5a * a + -4b * a) + 2b * (5a + -4b)) = 0

Reorder the terms:
((-4ab + 5a2) + 2b * (5a + -4b)) = 0
((-4ab + 5a2) + 2b * (5a + -4b)) = 0
(-4ab + 5a2 + (5a * 2b + -4b * 2b)) = 0
(-4ab + 5a2 + (10ab + -8b2)) = 0

Reorder the terms:
(-4ab + 10ab + 5a2 + -8b2) = 0

Combine like terms: -4ab + 10ab = 6ab
(6ab + 5a2 + -8b2) = 0

Solving
6ab + 5a2 + -8b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -4b)(a + 2b) = 0


Subproblem 1
Set the factor '(5a + -4b)' equal to zero and attempt to solve:

Simplifying
5a + -4b = 0

Solving
5a + -4b = 0

Move all terms containing a to the left, all other terms to the right.

Add '4b' to each side of the equation.
5a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
5a + 0 = 0 + 4b
5a = 0 + 4b
Remove the zero:
5a = 4b

Divide each side by '5'.
a = 0.8b

Simplifying
a = 0.8b

Subproblem 2
Set the factor '(a + 2b)' equal to zero and attempt to solve:

Simplifying
a + 2b = 0

Solving
a + 2b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2b' to each side of the equation.
a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
a + 0 = 0 + -2b
a = 0 + -2b
Remove the zero:
a = -2b

Simplifying
a = -2b
Solution
a = {0.8b, -2b}

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